Mechanical impedance measuring device



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IMPEDANCE MEQASURING DEVIQE 3 Sheets-Sheet l vw r R u NN w N :uw RN Inf, nnllrbll.. @N Sk Y FiledVV L !grch 30, 1943 :Summer I mf (Iitomeg NIU A. M. WIGGINS MECHANICAL IMPEDANCE MEASURING DEVICE AAug. 8, 1944.

3 Sheets-Sheet 3 Filed March 30 1943 hi" uw IUI HIL'XUpHHYU LY. lLkJllliUl .li Patented Aug. 8, 1944 MECHAICAL AIIVHEDANYCE MEASURING DEVICE Alpha M. Wiggins, Princeton, N. J., assigner to l Radio Corporation of America, a corporation of Delaware Application March 30, 1943, Serial No. 481,119

(Cl. 73--51l Claims.

This invention relates generally to apparatus for measuring mechanical impedance Aand more particularly to a device for determining the mechanical impedance of vibrating systems such as armatures, diaphragms, suspensions or sound translating devices.

If two substantially identical metallic reeds are driven by the same source and caused to vibrate in phase, fixed conductive plates disposed adjacent the vibrating reeds may provide separate variable capacitors analogous to condenser microphones. lf similar amplifying devices are connected to the separate reeds and their associated fixed capacitive plates, the Voutput of the two amplifiers will be substantially identical in frequency, amplitude and phase. If an additional mechanical element such as, for

' example, a device of which the mechanical impedance is to be determined, is applied to load one of the reeds, the amplitudeand phase of vibration of the reed will be substantially changed. Since the mass and compliance of the reeds may be determined'readily, the mechanical impedance of the loading device may be calculated from the difference in amplitude and phaseof the signals from the loaded and unloaded vibrating reeds.

If a reed, clamped at one end with the other end free, is driven at the'clamped end by alternating force, the displacements of the free end from the neutral position will be proportional to the applied force and the compliance of the reed. f The force acting on'the reed will be the effective mass times the acceleration. The effective' mass of a reed clamped at one end is cnefourth of its total mass; The equivalent circuit is a mass of one-fourth the total mass, shunted by a compliance, which is' equal to where L is the length of the reed, E the Youngs modulus, b the width and a.- the thickness of the reed. If two identical reeds are driven by the same force, the displacements of the free ends will be in phase and equal. Their relative displacements will therefore be Zero. If one reed is then loaded with a mechanical impedance at its free end, the relative vdisplacements will be proportional to the driving force. the mechanical impedance of the loading devices, the masses and the compliances of the reeds.

In a preferred modification of the invention, to be. described in detail hereinafter, the two reeds form the ground plates of condenser-s and may comprise a single reed rigidly clamped at its center. 'Ihe high potential capacitive plates disc c posed `adjacent the free ends of the reeds are fastened rigidly to the. driving mechanism. This driving mechanism may comprise a. conventional sound translating device such as, for example, a dynamic loudspeaker unit. The dimensions of the vibrating reeds are selected to provide suitable constants at the driving frequency. The

driving unit may be actuated by applying thereto from the two amplifiers are mixed in phase opposition, so that when the reeds-are driven with no load applied toeither reed, the two signals' may be cancelled. After the signals are balanced, and a load is applied to the free end of one of the reeds; the mixed signal will be proportional to the vectorial difference between the force on the loaded reed and the force on the unloaded reed. The mechanical impedance in ohms of the load will be proportional to the ratio of the mixed signal with one reed loaded and the signal from the unloaded reed.

Among the objects of the invention are to provide an improved means for measuring the me chanical impedance of a mechanical element. Another object is to provide an improved method of and means for measuring the mechanical impedance of a mechanical element wherein the loading effect of the mechanical element upon one of two substantially identical reeds is measured and the mechanical impedance calculated from the vectorial difference in displacement of the two reeds. Another object of the invention is to provide an improved method of and means for measuring the mechanical impedance of a mechanical element wherein two vibratory reeds provide electric potentials which may be balanced and wherein the mechanical element is caused. to load one of the reeds, thereby unbalancing the potentials derived from said reeds.

The invention will be described in greater detail by reference to the accompanying drawings of which Figure l is a schematic circuit diagram of the equivalent circuit of the loaded and unloaded vibratory reeds; Figure 2 is an elevational view of one embodiment of the invention, Figure 3 is a cross-sectional view along the section III, III of la. portion of Figure 2, Figure 4 is a sectional view of Figure 3 along the section IV, IV and Figure 5 is a schematic circuit diagram of the electrical circuit associated with the device illustrated in Figures 2 3 and 4. Similar reference numerals are applied to similar elements throughout the drawings.-

Referring to Figure 1, the equivalent circuit of the vibratory reeds lincludes a loading device suoliA as a phonograph pickup. The unknown irnpedance Zx .of the load may be calculated by using the ratio of the forces, and the masses and compliancesvof the reeds. Xm represents the reactanceof the mass of eithervrreed, X-cthe reactance of the compliance of either reed, Zi the equivalent impedance of the parallel mass and compliance of the unloaded reed, Zz the equivalent im pedan'ce of the mass of the loaded reed in series with the unknown impedance and shuntecl by the compliance of the loaded reed, Fi theforce on the unloaded reed as represented by the capacity variations it provides, and F2 the force on the loaded reed as represented by the capacity variations which it provides.

.which is true for frequencies well below the resonant frequency of the reed: the equation becomes:

Xm is 180 out of phase with so eliminating the vector quantities and using only the numerical quantities, the equation becomes:

` z2-z. VX2, (8) 'MFTl [xm-ir? Since Egli riz,

the equation may be written:

XA, Xe]

y gle as well as the magnitude of the mechanical l if, however, v

(Z2-Z1)Xm Z 1X C i y is not small in comparison to 1. 'I'he full equation,

must be taken into consideration with the phase relations. This equation will give the phase animpedance.

In operating the mechanical impedance bridge,

a reed adapted to be clamped at its center is selected for the frequency range desired and placed on the driving mechanism which is driven at the frequency at which the measurement is'to be made. With both reeds unloaded, the amplifier. outputs are balanced by adjusting the voltage amplitude of one until a substantially perfect balance is obtained. Then theload is. applied to one of the vibrating reeds and the amplifier Y outputs noted. The mechanical impedance may then be calculated from the equation:

v F2-Fx Xin] (l1) Z:c- Fl [Xm XC In order to facilitate'the calculation 0f the mechanical impedance by this formula, curves may be plotted of versus frequency for each reed, whereby the ratio (F 2- Fi) ments may be made at frequencies up to and including 8,000 cycles. For frequencies below 500 cycles, the reeds should 'preferably be made of brass, while for higher frequencies aluminum is preferable. In all cases, the reeds should be Vclamped tightly to the driving unit. The unitary construction of the reeds to be described hereinafter facilitates rigid clamping.

Referring to'Figures 2, 3 and 4, a driving unit comprising a conventional loudspeaker field assembly having a core I and pole pieces 2 provides a strong magnetic field across an air gap 3. It should be understood that the magnetic iield may be provided by a permanent magnet or an electro-Y magnet as desired. A conventional electro- Ydynamic driving coil 4 is supported by a flexible rubber diaphragm 5 in the air gap 3. The diaphragm may be supported in any desired manner by the eld structure. A cylindricalV metallic driving member 6 is mounted rigidly to the driving coil 4 and diaphragm 5 by means Aoi rivets'l. Additional stiffness and support may be provided -for the driving member 6 by means of a corrugated metallic supporting strip 8 which extends to suitable studs 9 attachedto the field structure. A pair of reeds comprising a single metallic plate I0, I0 clamped at its center by means of a clamp l I, is attached rigidly to the end oi the cylindrical amplifier tube 23.

re" A first fixed capacitive plate I4 is secured to the insulating member I3 adjacent one end of the clamped reeds ID, Ill' and a second fixed capacitive element I5 is similarly secured to the insulating element I3 adjacent the other free'end of the clampedl reed I0', whereby the two free ends of the clamped reed provide separate variable capacitive devices. An adjustable frequency oscillator, or other suitable source of driving Power,

' 20 is connected to the driving coil 4.

The device of which the mechanical impedance is to be determined, in this instance a' conventional phonograph pickup, is adjustably mounted upon a suitable support I6 so that the phonograph needle of the pickup may be inserted in a small depression in the free end of one of the vibrating capacitor devices associated with the vibrating reeds. A power supply 2I of conventional design vsupplies operating potentials for the various amplifier thermionic tubes. The fixed capacitive electrode I4 is connected through a rst coupling capacitor22 to the control electrode of a first A high potential is applied to the capacitor electrode I4 through a high resistance 24 which is connected to the output of the "power supply 2 I.

The output of the first amplifier tube 23 is connected to a xed contact of a first switch 25 and to the control electrode of a second amplifier tube 2B. The control electrode circuit of the second amplifier tube 26 includes a variable resistor 2,1 which is also connected to the movable contact of a second switch28. VThefixedcontacts of the second switch 28 are connected respectively to a plurality of graduated fixed-capacitors 29. The remaining terminals of the fixed capacitors 29 are connected to ground.

The output of the second amplifier 28 is coupled in a conventional manner to a control electrode of a tube 3U which is of the double diode-tried@ type. The anodes of the two diodes are connected together and connected through a third resistor 3I to one terminal of a first indicatimr mete-r 32. The remaining terminal of the indicating meter 32 is connected to the cathode of the diode-triode tube 30 through a cathode resistor 33. It is also connected to ground through a fourth resistor 34.

The remaining fixed contact of the first switch I 25 is connected to ground. AThe movable contact of the Yswitch 25 is connected to the control electrode of a third thermionic tube amplifier 35 The anode of the third thermionic amplifier' tube 35 is coupled to the control electrode of a second double diode-triode tube- 36. The two ancdes of the diodes of the diode-triode tube 36 are connected together and connected through a fifth resistor 31 to a second indicating meter 38.

Thel

remaining terminal of the second indicating meter DETCH iiUUll 38 is connected to the cathode of the double diodetriode tube through a second cathode resistor 39,

and is connected to ground through a sixth resistor 40.

The second fixed capacitor electrode I5 is connected through a second coupling capacitor 4I .Y

of a third switch 44. The fixed contacts of the third switch 44 are connected respectively to separate graduated fixed capacitors 46. The remaining terminals of the capacitors 46 are connected to ground. The output of the fifth amplifier tube `45 is connected across a potentiometer 4l. 'I'he movable contact of thev potentiometer 41 is con? nected to the control electrode of a sixth amplilier tube 48. tube 48 is connected to the anode of the third amplifier tube 35.

It should be understood that the first variable resistor 2l and second switch 28 with its associated capacitors 29 comprise a phase control for the amplifier system including the tubes 23, 26 and 3U. Likewise, the second variable resistor 43', the third switch 44 with its associated capacitors 46, comprise a phase control for the second amplifier'including the tubes 42, 45, 48 and 38.

The first switch 25' controls the application of signals from the first fixed capacitor electrode I3 to the third amplifier tube 35.

Inoperation, if the movable contact of the first switch 25 is connected to ground, the first meter 32 will provide an indication which is characteristic of the vibration of the end of -the reed- IU adjacent the first fixed capacitor electrode I4; and the second meter '38 willprovide indication characteristic of the vibration of the reed I0 adjacent the second fixed capacitive electrode I5. If the movable contact of thefirstswitch 25 is connected tothe ungrounded fixed switch terminal. signals derived from the flrst fixed capacitive electrode I4 will also be applied to the diode-triode tube 3S, and the indication' on the second meter 38 will be proportional to the difference between the signals derived from the two reeds. With both reeds unloaded by any ex-V ternal mechanical device, the outputs of the two capacitive pickup devices may be balanced as to amplitude by adjusting the position of the movable contact of the potentiometer 41. Similarly, the phases of the signals derived from the two reeds may be balanced -by adjusting the first variable resistor 2l and the movable contact of the second switch 28. or by adjusting the second variable resistor 43 and the movable contact of the third switch 44. Provision is made for shifting the phases of the signals derived from the separate reeds, because of a slight rocking motion which may occur in the driving mechanism at some frequencies. This rocking motion provides a small phase displacement between the signals which would prevent the cancellation or balancing of no-load signals. After the circuit is balanced for the signals derived from both unloaded reeds, one of the reeds is loaded and the readings then derived from the first and second meters 32, 38, respectively, 'are substituted in Equation l1 to determine the me- The anode of the sixth amplifierV means for determining the mechanical impedance of mechanical elements by utilizing the loading effect of said elements upon one of a pair of vibrating reeds which are connected to a balanced electrical circuit.

I claim as my invention: l l. Apparatus for measuring the mechanica impedance of a movable mechanical element wherein said apparatus includes a vibratory driving device, means for connecting to said device a source of 'power for actuating said vibratory device at a predetermined frequency, a pair of similarly tuned vibratory elements having substantially equal predetermined inertiasand compliences, one of said pair of vibratory elements having means adapted to receive said mechanical element to b e measured, means including said driving device for providing forced vibra-y tion of both of said tuned elements, means for deriving potentials in response to said vibration of said tuned elements, means for balancing said potentials, means. for supporting said movable mechanical element in operable relation with said 'one of said tuned elements to load said ele-v ment to provide unbalance of said potentials,

and means for indicating said mechanical impedance of said movable mechanical element in terms of said unbalanced potentials and said predetermined inertias and said compliances of said tuned elements.

2. Apparatus for measuring the mechanical impedance oi. a movable mechanical element wherein said apparatus includes a vibratory driving device, meansfor connecting to said device a source of power for actuating said vibratory device at a predetermined frequency, a pair of similarly tuned vibratory elements having substantiallyequal predetermined inertias and compliances, one of said pair of vibratory elements having means adapted'to receive said mechanical element to be measured, means including said driving device for providing forced vibration of both of said tuned elements, means including a pair of reactive. pickup elements for deriving potentials in response to said vibration of said tuned elements, means for balancing said poten- 'tialsg means for supporting said movable mechanical element in operable relation with said one of said tuned elements to load said element to provide unbalance Yof saidpotentials, and

" .means for indicating said mechanical irnpedance of said movable mechanical element in terms of said unbalanced potentials and said predetermined inertias and said compllances of said tuned elements.

3. Apparatus for measuring the mechanical impedance of a movable mechanical element wherein said apparatus includes a vibratory driving device, means for connecting to said device a source of power for actuating said vibra-l tory device at a predetermined frequency, a pair of similarly tuned vibratory elements having substantially equal predetermined inertias and with said one of said tuned elements to load said element to provide imbalance of said potentials, and means for indicating said mechanical impedance of said movable mechanical element in terms of said unbalanced potentials and said predetermined inertias and said, compliances of said tuned elements.

V4. Apparatus. of the type described in claim 1 including means for controlling separately the amplitudes of eac-h of said potentials.

5.v Apparatus of the type described in claim 1 including means for controlling separately the phases of each of said potentials, s

6. Apparatus ofthe type described in claim 3 including means for controlling separately the amplitudes o f said potentials and means for adjusting separately the phases `of said potentials. Y

7. Apparatus for measuring the mechanical impedance of a movable mechanical element i wherein said apparatus includes "a vibrator-y driving device, means for connecting to said device a source of power for actuating said vibrator-y vdevice at a predetermined frequency, a pair of similarlytuned vibratoryA elements having substantially equal predetermined inertias and compliances, one of said pair of vibratory elements having means adapted to receive said mechanical element to be measured, means including said driving device for .providing forced vibration of both of said tuned elements, means including av pair of capacitive pickup elements for deriving potentials in response to said vibration of said tuned elements, means for balancing said potentials, meansfor supporting said movable mechanical element in operable relation with said one of said tuned elements to load said element to provide unbalance of said potentials, and means for indicating said mechanical impedance of said movable mechanical element in terms of said unbalanced potentials and said predetermined inertias and said compliances' of said tuned elements'. l

8. Apparatus of the type described in claim 3 characterized in that said vibratory elements comprise asingle elongated metallic member, and means supporting and driving said member .at a node thereof.

9. Apparatus of the type describedin claiml 3 characterized in that said potential deriving means-are supported by said vibratory device.

l0. Apparatus for measuring themechanical impedance of a sound translating element wherein said apparatus includes a vibratory driving device, means for connecting to said device a l source of power for actuating said vlbratory device at a predetermined frequency, a pair of similarly tuned vibrator-y elements having substantially equal predetermined inertias and compliances, one of said pair of rvibratory elements having means adapted to receive said sound translating element to be measured, means including said vdriving device for providing forced vibration of both of said tuned elements, means for deriving potentials in response to said vibration of said tuned elements, means for balancing'said potentials, means for supporting said sound trans` lating element in operable relation with said one .n of saidtuned elements to load said element to provide imbalance of said potentials, and. means mentsh for indicatir'igv said mechanical impedance of said sound translating element in terms of said unbalanced potentials and said predetermined inertias and said compliances of said tuned ele- ALPI-IA M. WIGGIN S. 

